> LLMs by design are not capable of reason.
This isn't true.
A deep neural network certainly can emulate the logical functions we think of as "reasoning" (ie, AND/OR/XOR functions).
See for example:
https://cprimozic.net/blog/boolean-logic-with-neural-network...
https://www.cs.toronto.edu/~axgao/cs486686_f21/lecture_notes...
https://towardsdatascience.com/emulating-logical-gates-with-...
https://medium.com/@stanleydukor/neural-representation-of-an...